1What does SINE stand for?
Search
Interchange
Normalize
Eliminate
2What are the methods to get the inverse of a matrix?
Gauss-Jordan Method
Adjoint Method
3What do you call the matrix made from a system of linear equations
Augmented Matrix
4What are the methods of solving linear equations?
Gauss-Jordan Method
Gaussian Elimination Method (Backsubstitution)
Cramer's Rule (Upto 3x3)
5A _ is a number associated with a square matrix.
Determinant
6What are the theorems of determinants in any order?
1. (Number of terms) The number of terms in the expansion of a determinant is n!
2. (Interchanging) If any two columns or rows are interchanged, the determinant is changed.
3. (Zero) If all elements in any row or column is zero, its value is zero.
4. (Equality and proportionality) If two columns or rows have corresponding elements that are identical or proportional, its value is zero.
7What are the methods to expand a determinant?
Basket and Triangle Method (3x3)
Minors and Cofactors Method
Pivot Method
Laplace Development Method
8What is a minor and what is a cofactor?
The cofactor is the formula involving the (-1)^(i+j) Mij. The minor is Mij and it includes all the elements NOT touched by the imaginary lines.
9The value of the determinant is the algebraic sum of the products obtained by multiplying each element of a column or a row by its cofactor or a signed minor.
Expansion of Determinants by Minors
10If the given determinant has an element equal to one or unity, this element is the pivotal element. Cross out the row and column through aij. What method is this?
Expansion of Determinants by the Pivotal Method
11In this methood we can directly determine if the matrix is invertible or not. If the value of the determinant is zero, the matrix is singular or no inverse. Otherwise the matrix is invertible.
Inverse of a Matrix Using Adjoint Matrix
12A method in solving linear equations which involves the use of determinants.
Cramer's Rule
13Let D be an nth order determinant and let m be the Kth order determinant whose elements are those in any K rows and columns of D. Then M is called the Kth minor of D.
Laplace Development